Golf club shaft simulation method

ABSTRACT

A computer-aided golf club shaft swing simulation method, includes: dividing a model of a shaft into a plurality of model areas continuously along its length from a proximal end to a distal end thereof; inputting values of Young&#39;s modulus, modulus of elasticity in shear and geometrical moment of inertia into the plurality of model areas or their joint portions; and analyzing a behavior of the shaft when the shaft is swung according to a given swing pattern.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2007-220919, filed Aug. 28, 2007, the entire contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates to a computer-aided golf club shaft simulation method and more particularly to a simulation method for analyzing the behavior of a golf club shaft when it is swung.

Conventionally, in studying the behavior of a golf club shaft when it is swung, it is common practice that a plurality of strain gauges are attached to the shaft, so that the amount of strain of the shaft is measured by these strain gauges (refer to, for example, JP-A-2003-205053 and JP-A-2003-284802).

With the methods of JP-A-2003-205053 and JP-A-2003-284802, however, since lead wires are connected respectively to the plurality of strain gauges attached to the shaft, the golf club gets heavy, and this makes it difficult for a golfer to swing the golf club. Because of this, it is difficult for the golfer to make identical swings, and hence, it has been difficult to measure the amount of strain of the shaft through repetition of identical swings.

In addition to them, JP-A-2002-331060 proposes a golf club swing simulation method as the method for analyzing the behavior of a golf club. In this method, a golfer's swinging behavior is measured using a true golf club, so as to obtain coordinate time history data of a grip of the golf club when the golf club is swung by the golfer, time history data of the inclination angle of the grip, time history data of the rotational angle of the grip round the shaft's axis which is a geometrical center axis of the shaft, and a swinging motion is given to a golf club model based on the three time history data, so as to analyze the behavior of the golf club through simulation in consideration of twisting of the golf club model (See claim 1 of JP-2002-331060).

With the method of JP-A-2002-331060, however, since many data such as the properties of shaft materials, shaft's volume and shaft's diameter are inputted into the computer, the simulation takes time.

SUMMARY OF THE INVENTION

The invention has been made in view of the situations and an object thereof is to provide a golf club shaft simulation method which can perform a simple and accurate simulating calculation by inputting fewer parameters into a computer.

The invention provides a computer-aided golf club shaft swing simulation method, including: dividing a model of a shaft into a plurality of model areas continuously along its length from a proximal end to a distal end thereof; inputting values of Young's modulus, modulus of elasticity in shear and geometrical moment of inertia into the plurality of model areas or their joint portions; and analyzing a behavior of the shaft when the shaft is swung according to a given swing pattern.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an explanatory diagram showing a state in which a shaft is divided into a plurality of model areas.

FIG. 2 is a graph showing a change with time in head angular speed in each of various types of swing patterns.

FIG. 3 is a explanatory diagram showing a two-link model which configures the various types of swing patterns.

FIG. 4 is a graph showing the results of analysis of speed differences of shafts between distal end and proximal end according to the invention.

FIG. 5 is a graph showing the results of analysis of dynamic lofts according to the invention.

FIG. 6 is a graph showing the results of analysis of face angles according to the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In this embodiment, since Young's modulus, modulus of elasticity in shear and geometrical moment of inertia which are associated with bending rigidity and torsional rigidity of the shaft are selected as parameters to be inputted into the computer, a simple and accurate simulation can be implemented by inputting the few parameters. In addition, since there are few parameters to be inputted into the computer, the parameters can easily be changes so verify a change in the behavior of the shaft on the spot, so that the results of the simulation can of help to the design of a golf club quickly.

Hereinafter, the embodiment will be described in greater detail. In this embodiment, the shaft is divided into the plurality of model areas continuously along its length from the proximal end to the distal end thereof, and values of Young's modulus, modulus of elasticity in shear and geometrical moment of inertia are inputted into the plurality of model areas or their joint portions. As this occurs, it is appropriate that the shaft is divided into 5 to 20 model areas along its length from the proximal end to the distal end thereof. In addition, assuming that an area of the shaft which lies 5 to 20 cm away from the proximal end is a first model area, the shaft can then be divided into a plurality of model areas of the same length along the length from a distal end of the first model area to the distal end of the shaft.

In the embodiment, the Young's modulus, modulus of elasticity in shear and geometrical moment of inertia are inputted into the plurality of model areas. Values of Young's modulus, modulus of elasticity in shear and geometrical moment of inertia can be obtained as below.

[Young's Modulus, Geometrical Moment of Inertia]

An EI value is such as to constitute a pilot value for bending rigidity, and an EI value can be obtained by performing a three-point bending test. Values of Young's modulus (E) and geometrical moment of inertia (I) can be obtained from this EI value. Specifically, a shaft is horizontally supported by a pair of supporting tools which are spaced a certain distance (L) apart from each other, a load (P) is exerted vertically on a central position between both the supporting pints (the supporting tools), and an amount of strain (σ) at the central position is obtained.

EI=(L ³/48)·(P/σ)(kg·mm²×10⁶)

-   L: Distance between both the supporting tools (mm) . . . 300 mm -   P: Load exerted vertically on the shaft (Kg) . . . 20 Kg -   σ=Amount of strain when the load is exerted (mm)

A geometrical moment of inertia can be obtained by a computational expression from the cross section of the shaft.

I=π×(d ⁴ −d1⁴)/64

-   d: Outside diameter of the shaft -   d1: Inside diameter of the shaft

A Young's modulus (E) can be obtained from the result of the above computational expression.

E=(L ³/48)·(P/σ)(kg·mm²×10⁶)/I

[Modulus of Elasticity in Shear]

Firstly, to obtain a modulus of elasticity in shear, a torque is obtained in each portion. Namely, a certain portion of the shaft is fixed in such a manner as to permit no rotation, a constant rotating force is exerted on a location which is spaced apart from the fixed portion of the shaft in a certain direction, that is, in a direction towards the distal end or a direction towards the proximal end of the shaft, and an angle through which the location to which the rotating force was exerted rotates is measured. In this embodiment, the shaft is fixed in the fixed position by a chuck, a rotating force (1 ft·1 bt: 138.25 kgf·mm: 1.35 N·m) is then exerted on a location which is spaced 100 mm apart from the fixed position, and an angle through which the rotating force exerted location has rotated is measured.

T=G·Ip(x)·dθ/dx

-   T: Torque (torsional moment) -   G: Modulus of elasticity in shear -   IP(x): Polar moment of inertia of area -   dθ/dx: rotational angle per unit

A polar moment of inertia of area can be obtained from the section of the shaft by a computational expression.

Ip(x)==π×(d ⁴ −d1⁴)/32

-   d: Outside diameter of the shaft -   d1: Inside diameter of the shaft

Consequently, a modulus of elasticity in shear can be obtained from the following expression.

G=T/(Ip(x)·dθ/dx

In this embodiment, club head weight, gravity center distance and gravity center depth can be added to factors that are inputted for simulation, whereby a load can be reproduced that would be exerted on a shaft of a true golf club when the true golf club is swung. In addition, a simulation can be implemented for enabling a shaft design matched to the characteristics of a club head.

In the embodiment, by adding club head weight, gravity center distance, gravity center depth and gravity center height to factors that are inputted for simulation, a dynamic loft and face angle at the time of impact, which will be described later, can be outputted, whereby the conditions of the head at the time of impact can be estimated.

Hereinafter, while an embodiment of the invention will be described by reference to the drawings, the invention is not limited to the following embodiment. As is shown in FIG. 1, on the computer, a shaft 10 was divided into a plurality of model areas (10 areas, in this embodiment) 12 along its length from a proximal end to a distal end thereof and a club head 14 was attached to the distal end of the shaft 10. Then, as input parameters, shaft weight, Young's modulus, geometrical moment of inertia and modulus of elasticity in shear, as well as club head weight, gravity center distance and gravity center depth were inputted. In this case, the Young's modulus, geometrical moment of inertia and modulus of elasticity in shear of the shaft, which are parameters as an elastic element, were inputted in joint portions 16 between the respective model areas 12, whereby the shaft 10 was represented as an elastic element. In this embodiment, as the shaft 10, the following five kinds of shafts were prepared.

-   STD: Standard shaft -   TipDown: Shaft with low Young's modulus at the distal end -   TipUp: Shaft with high Young's modulus at the distal end -   ButtDown: Shaft with low Young's modulus at the proximal end -   ButtUp: Shaft with high Young's modulus at the proximal end

In addition, as is shown in FIG. 4, four types of swing patterns were inputted into the computer. “acceleration: large” is a swing pattern in which the acceleration of the head angular speed just prior to impact is large, “acceleration: small” is a swing pattern in which the acceleration of the head angular speed just prior to impact is small, “deceleration: large” is a swing pattern in which the deceleration of the head angular speed just prior to impact is large, and “deceleration: small” is a swing pattern in which the deceleration of the head angular speed just prior to impact is small.

In this case, as is shown in FIG. 3, a first link 20 corresponding to an upper arm portion, a second link 22 corresponding to a lower arm portion, a shaft portion 24 and a head portion 26 were coupled together, and a first rotating motion 28 which implements the overall rotating motion was set at an upper end portion of the first link 20 and a second link model 32 in which a second rotating motion 30 for reproducing a cock by the wrists is disposed in a connecting portion between the first link and the second link were constructed on the computer, whereby the four types of swing patterns were configured by adjusting the rotational speeds by the first rotating motion 28 and the second rotating motion 30.

The behaviors of the shafts were analyzed when the five kinds of shafts were swung in the four types of swing patterns. In this case, the shafts 10 were swung while inclined 50° relative to a horizontal plane. In addition, the head speed at the distal end portion of the shaft was set to be 45 m/s with the angular speed of the proximal portion of the shaft maintained constant and when assuming that the shafts would not flex. As output parameters, a difference in speed between the distal end and proximal end of the shaft, dynamic loft and face angle were outputted.

The results of analysis of speed difference of the respective shafts between the distal end and proximal end are shown in FIG. 4. The speed difference between the distal end and proximal end of the shaft represents an estimated speed at the distal end of the shaft with the speed at the proximal end of the shaft remaining the same and represents an amount of increase or decrease in head speed that is obtained by the properties of the shaft when the same kinetic momentum is inputted into the shaft. In FIG. 4, the value of a speed difference of the standard shaft (STD) is indicated as being 1. It can be said from FIG. 4 that in most of the swing patterns excluding the swing pattern in which the acceleration is large just prior to impact (acceleration: large), the speed at the distal end becomes faster than that at the proximal end with the values of rigidity being low at the distal end and the proximal end, expecting an increase in head speed. In particular, the reduction in rigidity at the distal end tends to influence largely the effect of increasing the head speed.

The results of analysis of dynamic lofts were shown in FIG. 5. The dynamic loft is a loft (based on the horizontal plane) at the moment of impact and represents the angle of a trajectory of a ball hit, that is, ease with which the ball soars. In FIG. 5, indicating the dynamic loft of the STD as being 0° (standard), differences or deviations from the dynamic loft of the STD are shown. In FIG. 5, while, as a matter of convenience in representation, the dynamic loft of the STD is shown as being 0°, in reality, the dynamic loft of the STD has a specific value other than zero. It is seen from FIG. 5 that the tendency that the lower the rigidity at the distal end, the larger the dynamic loft is constant irrespective of the swing modes and that the tendency of rigidity at the proximal end changes depending upon the swing modes.

The results of analysis of face angles are shown in FIG. 6. The face angle here means a face angle at the moment of impact and represents ease with which a ball is caught. In FIG. 6, indicating the face angle of the STD as being 0° (standard), differences or deviations from the face angle of the STD are shown. It is seen from FIG. 6 that in the case of the swing pattern in which the head angular speed decelerates at the time of impact, with low rigidity at the distal end, the face is largely closed (directed to the left).

The following become obvious from the results of the simulations described above. With some of the output parameters, the tendency is not changed, while with others, the tendency is changed by the relationship between swing pattern and shaft rigidity distribution, and consequently, the importance of bending rigidity and torsional rigidity that are possessed by the portions of the shaft are made clear by the simulation method of the embodiment, whereby the design of a shaft having target properties or the design of a shaft matching a specific swing pattern is enabled. Thus, the simulation method of the embodiment can be of help to the design of golf clubs.

As described with reference to the embodiment, there is provided a golf club shaft simulation method which can perform a simple and accurate simulating calculation by inputting fewer parameters into a computer.

In the embodiment, by setting the mechanical factors (bending rigidity, torsional rigidity) of the shaft in the respective model areas aligned in the longitudinal direction, the flexure and torsion of the shaft in swing are studied on the computer, whereby it becomes possible to know how the flexure and torsion of the shaft change depending upon different swing patterns. In addition, by adding the data of a head which is attached to the shaft, information at the time of impact can be obtained. By giving shaft data in each portion, the respective factors can be made to approach their optimal values from the size of the head or the like by this simulation method, thereby making it possible to implement a shaft design in a short period of time. 

1. A computer-aided golf club shaft swing simulation method, comprising: dividing a model of a shaft into a plurality of model areas continuously along its length from a proximal end to a distal end thereof; inputting values of Young's modulus, modulus of elasticity in shear and geometrical moment of inertia into the plurality of model areas or their joint portions; and analyzing a behavior of the shaft when the shaft is swung according to a given swing pattern.
 2. The computer-aided golf club shaft swing simulation method as claimed in claim 1, wherein the model of the shaft is divided into 5 to 20 model areas along its length from the proximal end to the distal end thereof.
 3. The computer-aided golf club shaft swing simulation method as claimed in claim 1, wherein assuming that an area of the shaft which lies 5 to 20 cm away from the proximal end is a first model area, the model of the shaft is divided into a plurality of model areas of the same length along the length from a distal end of the first model area to the distal end of the shaft.
 4. The computer-aided golf club shaft swing simulation method as claimed in claims 1, wherein club head weight, gravity center distance and gravity center depth are added to factors to be inputted for simulation. 